Several of the winterbash hats have criteria that are "non-binding," for example "Witticism" requires 5 upvoted questions.

If such a criteria no longer applies, such as an upvoted question or answer getting downvoted later and no longer qualifying for a hat, will the user keep the affected hat or will it no longer be available?

Why would it? Considering that non-tag badges aren't even revoked for things like this and that the hats will only exist for a couple weeks, do you really think they built processes to revoke hats, of all things?